South Korea and West Germany are atypically good performers for Capitalist world, which has its growth failure stories like India, Indonesia, Peru, Chile, Argentina, UK, and New Zealand (going from extreme poor to extreme rich).

Most of those countries were not capitalist, but rather socialist mixed economies. New Zealand is actually rather capitalistic, and has respectable growth for an advanced economy and persistent low unemployment, so I'm not sure what you're getting at there. Here's Wikipedia on India:

Indian economic policy after independence was influenced by the colonial experience (which was seen by Indian leaders as exploitative in nature) and by those leaders' exposure to Fabian socialism. Policy tended towards protectionism, with a strong emphasis on import substitution, industrialization, state intervention in labor and financial markets, a large public sector, business regulation, and central planning.[8] Five-Year Plans of India resembled central planning in the Soviet Union. Steel, mining, machine tools, water, telecommunications, insurance, and electrical plants, among other industries, were effectively nationalized in the mid-1950s.[9] Elaborate licences, regulations and the accompanying red tape, commonly referred to as Licence Raj, were required to set up business in India between 1947 and 1990.

India liberalized starting in the 1980s but mostly since 1991. Growth accelerated rapidly after the state declared bankruptcy (basically) in 1990 and liberalization began. When Chile liberalized its economy, it went from one of the poorest to the wealthiest country in Latin America, which strongly refutes your hypothesis.

Dividing countries into two categories, as TGGP says, is not the best option. Most countries aren't fully capitalist or communist but rather a mix. On the one extreme you have countries like Singapore, Switzerland and Hong Kong, on the other you have North Korea.